{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forrest Fire (Protugal) prediction using SVR, Random Forest, and Deep NN\n",
    "\n",
    "This dataset is public available for research. The details are described in [Cortez and Morais, 2007]. Please include this citation if you plan to use this database:\n",
    "\n",
    "P. Cortez and A. Morais. ***A Data Mining Approach to Predict Forest Fires using Meteorological Data.*** \n",
    "In J. Neves, M. F. Santos and J. Machado Eds., New Trends in Artificial Intelligence, Proceedings of the 13th EPIA 2007 - Portuguese Conference on Artificial Intelligence, December, Guimaraes, Portugal, pp. 512-523, 2007. APPIA, ISBN-13 978-989-95618-0-9. \n",
    "  \n",
    "Available at: http://www.dsi.uminho.pt/~pcortez/fires.pdf\n",
    "\n",
    "For more information, read [Cortez and Morais, 2007].\n",
    "\n",
    "* X - x-axis spatial coordinate within the Montesinho park map: 1 to 9\n",
    "* Y - y-axis spatial coordinate within the Montesinho park map: 2 to 9\n",
    "* month - month of the year: \"jan\" to \"dec\" \n",
    "* day - day of the week: \"mon\" to \"sun\"\n",
    "* FFMC - FFMC index from the FWI system: 18.7 to 96.20\n",
    "* DMC - DMC index from the FWI system: 1.1 to 291.3 \n",
    "* DC - DC index from the FWI system: 7.9 to 860.6 \n",
    "* ISI - ISI index from the FWI system: 0.0 to 56.10\n",
    "* temp - temperature in Celsius degrees: 2.2 to 33.30\n",
    "* RH - relative humidity in %: 15.0 to 100\n",
    "* wind - wind speed in km/h: 0.40 to 9.40 \n",
    "* rain - outside rain in mm/m2 : 0.0 to 6.4 \n",
    "* area - the burned area of the forest (in ha): 0.00 to 1090.84\n",
    "\n",
    "**As we will see this is a extremely hard regression problem with clear outliers which cannot be predicted using any reasonable method. Four methods: (a) support vector regression, (b) decision tree, (c) random forest, (d) 3-layer dense neural network will be tried to show the relative performance.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read the Forest Fire dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>FFMC</th>\n",
       "      <th>DMC</th>\n",
       "      <th>DC</th>\n",
       "      <th>ISI</th>\n",
       "      <th>temp</th>\n",
       "      <th>RH</th>\n",
       "      <th>wind</th>\n",
       "      <th>rain</th>\n",
       "      <th>area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>mar</td>\n",
       "      <td>fri</td>\n",
       "      <td>86.2</td>\n",
       "      <td>26.2</td>\n",
       "      <td>94.3</td>\n",
       "      <td>5.1</td>\n",
       "      <td>8.2</td>\n",
       "      <td>51</td>\n",
       "      <td>6.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>oct</td>\n",
       "      <td>tue</td>\n",
       "      <td>90.6</td>\n",
       "      <td>35.4</td>\n",
       "      <td>669.1</td>\n",
       "      <td>6.7</td>\n",
       "      <td>18.0</td>\n",
       "      <td>33</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>oct</td>\n",
       "      <td>sat</td>\n",
       "      <td>90.6</td>\n",
       "      <td>43.7</td>\n",
       "      <td>686.9</td>\n",
       "      <td>6.7</td>\n",
       "      <td>14.6</td>\n",
       "      <td>33</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>mar</td>\n",
       "      <td>fri</td>\n",
       "      <td>91.7</td>\n",
       "      <td>33.3</td>\n",
       "      <td>77.5</td>\n",
       "      <td>9.0</td>\n",
       "      <td>8.3</td>\n",
       "      <td>97</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>mar</td>\n",
       "      <td>sun</td>\n",
       "      <td>89.3</td>\n",
       "      <td>51.3</td>\n",
       "      <td>102.2</td>\n",
       "      <td>9.6</td>\n",
       "      <td>11.4</td>\n",
       "      <td>99</td>\n",
       "      <td>1.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   X  Y month  day  FFMC   DMC     DC  ISI  temp  RH  wind  rain  area\n",
       "0  7  5   mar  fri  86.2  26.2   94.3  5.1   8.2  51   6.7   0.0   0.0\n",
       "1  7  4   oct  tue  90.6  35.4  669.1  6.7  18.0  33   0.9   0.0   0.0\n",
       "2  7  4   oct  sat  90.6  43.7  686.9  6.7  14.6  33   1.3   0.0   0.0\n",
       "3  8  6   mar  fri  91.7  33.3   77.5  9.0   8.3  97   4.0   0.2   0.0\n",
       "4  8  6   mar  sun  89.3  51.3  102.2  9.6  11.4  99   1.8   0.0   0.0"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('../Datasets/forestfires.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic statistics and visualization of the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Describe the statistics of numerical columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>FFMC</th>\n",
       "      <th>DMC</th>\n",
       "      <th>DC</th>\n",
       "      <th>ISI</th>\n",
       "      <th>temp</th>\n",
       "      <th>RH</th>\n",
       "      <th>wind</th>\n",
       "      <th>rain</th>\n",
       "      <th>area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "      <td>517.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.669246</td>\n",
       "      <td>4.299807</td>\n",
       "      <td>90.644681</td>\n",
       "      <td>110.872340</td>\n",
       "      <td>547.940039</td>\n",
       "      <td>9.021663</td>\n",
       "      <td>18.889168</td>\n",
       "      <td>44.288201</td>\n",
       "      <td>4.017602</td>\n",
       "      <td>0.021663</td>\n",
       "      <td>12.847292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.313778</td>\n",
       "      <td>1.229900</td>\n",
       "      <td>5.520111</td>\n",
       "      <td>64.046482</td>\n",
       "      <td>248.066192</td>\n",
       "      <td>4.559477</td>\n",
       "      <td>5.806625</td>\n",
       "      <td>16.317469</td>\n",
       "      <td>1.791653</td>\n",
       "      <td>0.295959</td>\n",
       "      <td>63.655818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>18.700000</td>\n",
       "      <td>1.100000</td>\n",
       "      <td>7.900000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.200000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>0.400000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>90.200000</td>\n",
       "      <td>68.600000</td>\n",
       "      <td>437.700000</td>\n",
       "      <td>6.500000</td>\n",
       "      <td>15.500000</td>\n",
       "      <td>33.000000</td>\n",
       "      <td>2.700000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>91.600000</td>\n",
       "      <td>108.300000</td>\n",
       "      <td>664.200000</td>\n",
       "      <td>8.400000</td>\n",
       "      <td>19.300000</td>\n",
       "      <td>42.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.520000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>92.900000</td>\n",
       "      <td>142.400000</td>\n",
       "      <td>713.900000</td>\n",
       "      <td>10.800000</td>\n",
       "      <td>22.800000</td>\n",
       "      <td>53.000000</td>\n",
       "      <td>4.900000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.570000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>9.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>96.200000</td>\n",
       "      <td>291.300000</td>\n",
       "      <td>860.600000</td>\n",
       "      <td>56.100000</td>\n",
       "      <td>33.300000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>6.400000</td>\n",
       "      <td>1090.840000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "                X           Y        FFMC         DMC          DC         ISI  \\\n",
       "count  517.000000  517.000000  517.000000  517.000000  517.000000  517.000000   \n",
       "mean     4.669246    4.299807   90.644681  110.872340  547.940039    9.021663   \n",
       "std      2.313778    1.229900    5.520111   64.046482  248.066192    4.559477   \n",
       "min      1.000000    2.000000   18.700000    1.100000    7.900000    0.000000   \n",
       "25%      3.000000    4.000000   90.200000   68.600000  437.700000    6.500000   \n",
       "50%      4.000000    4.000000   91.600000  108.300000  664.200000    8.400000   \n",
       "75%      7.000000    5.000000   92.900000  142.400000  713.900000   10.800000   \n",
       "max      9.000000    9.000000   96.200000  291.300000  860.600000   56.100000   \n",
       "\n",
       "             temp          RH        wind        rain         area  \n",
       "count  517.000000  517.000000  517.000000  517.000000   517.000000  \n",
       "mean    18.889168   44.288201    4.017602    0.021663    12.847292  \n",
       "std      5.806625   16.317469    1.791653    0.295959    63.655818  \n",
       "min      2.200000   15.000000    0.400000    0.000000     0.000000  \n",
       "25%     15.500000   33.000000    2.700000    0.000000     0.000000  \n",
       "50%     19.300000   42.000000    4.000000    0.000000     0.520000  \n",
       "75%     22.800000   53.000000    4.900000    0.000000     6.570000  \n",
       "max     33.300000  100.000000    9.400000    6.400000  1090.840000  "
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### Plot scatterplots and distributions of numerical features to see how they may affect the output 'area'\n",
    "\n",
    "For this, first we need to transform the outcome 'area' by taking its logarithm (after adding 1 to avoid zeros)\n",
    "\n",
    "$$\\text{Log-area} = log_{10}(area+1)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df['Log-area']=np.log10(df['area']+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZVX1NZd6Q57j7iagpC6NgtVRvOtSsplKQoIplmKFmxRJ1BmWxWB1hprFWQNDq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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa680b9908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Vi8g0NWQ9Qlh7nN453lNQe9wqctar5N43pWMiTxIlqlkNInI9cIWqfja4fxNw\nsaremnHMFCCpqgkRuQr4G1U9K8/fWgOsAWhoaFi0adOmU44rkUhQV1d3yo+fCAePdtPR1UdDDRzu\nhvq6Scye6uaF5rc63ud4Tz9AOl6AKdWVnFl/WoyRnezIid50AsiM9Ywp1cyc7FaPrLt/kNePdJFU\nTcdaJsKHZ9ZS43hVVx8+Y0NKKdbly5fvVtWWkY6L8nTuADAn435T0Jamqsczfn5cRP6fiMxQ1fdy\njrsPuA+gpaVFly1bdspBbd++nbE8Pmpth0/w+3/1M6CC288bYMPeCiDJT7+0yLndwQBuvPdZng2u\nH3wQLyyZP50Hr1sSZ2gn2frSQTY8+AsgO9a7bzyPZRfMjjO0k7QdPsHn/+pnQHasP/3SRU6+DzK5\n/hnLZLGeLMrhoxeAs0RkvohMAj4FPJp5gIicIcHKLBG5KIinI6qAJnJV4Klq3X+0oPa4NU6vLqg9\nTks+Ul9Qe5x8K3diikdkSUFVB4BbgX8DXgU2q+o+EblZRG4ODrseeFlEXgK+CXxKIxrP8qU2/byQ\nIZew9rg1N4WUow5pj1u+CrQuappeg5TlrGwvE2fXq5jiEelkclV9XFXPVtWPqOpfBm33qOo9wc93\nq+pCVb1AVRer6s+jiMOn2vSVFeXkfk+VS6rdRc+9kb9jF9YeJ59Wi/u2XsUUD/emiERgaFVgDx/M\nRx9aFejah6x2Ujk5a5YYVJwtmXzgaP6ZO2HtcWqaXkPPQPbwS8/AoLNn3xM9FdG4K3Po2+cpqc7w\nqXSEb2PJVSE9mLD2uOWOTrpeU8jWqxgriBcBn7rivo0lz6jLv5lOWHuc2ju7qanM7hzXVFY4OXw0\nxIfJESY6VhAvQr6UjvApgQF85PT886bD2uPk2/DRltYDXLL+SV4/0sUl692dHGGiE0dBvJK4puAb\nn8aSp52WvxpqWHvcfBk+GqqS2h9USe0dSHL7Qy+xdMEMp98PZnwVVUE81/gyJdU3586eWlB7nNo7\nuynP2bCoXMTJ4SOrkmognpGDkkgKPk1JBb8SmE9TaGsnldOb80XbO6iOzuyyKqkmZaKHvksiKcQx\nLneqfEtgTdNryB2AUdzcS/jgsfz/v8Pa47Rw9hQqcj6dFWVWJbVUTeQstJJICj5NSfUpgQF0dvWR\nzMkKSU21u+Z4d39B7XGqr6virlXNVFVIsEezcNeqZrueYCJXEknBp03QfUpg4Fetpik1+afJhrXH\nbWVzIz+z9a1aAAAKXklEQVRfdzkfnlnLz9dd7uyMOVNcSiIpwNBmJZp1z0X1dVWsWtSU1baqpcnJ\nBAYwPWSWUVh7nGZPzV+kL6zdBbZ4zUy0kkgKQ+P0vQND0/vU2XH6jkQvD76wP6vtwef3OxkrwP6Q\nYa2w9jh19Q3mvSju6mpxsMVrZuKVRFLwaZzet6mIPq1o9q2uVGrx2hPB4rUnnJ6FZopHSSSFpuk1\ndPUNZLV19Q04Ok7v11TEJR+ZUVB7nLr6BqmuzH7LV1eWOdlT6Ej0cvvm1qze7W2bW63HYCJXEknB\npxkyPk5F9GmPgsGcN8JgUp08Odh38DgD2fMNGEim2o2JUkkkBZ9myPg2FbG9s5vynAJ+5WVurhIG\nGMgZP8q9746wuFyN1xSLkkgKzXNCdgcLaY/byuZGHvvCZcyeVsNjX7jM6amItZPK6enPPqXt6U86\nOU6/7+DxvAvtXDz7Xjh7at4e2EIHy4eY6E3khIOSSAoLGiazesncrLbVS+Y6uwH6ltYDXHP3Dg4d\n7eaau3c4fYHx4LH8m+mEtcfLn7Pv+roqNtxwQdbamg03XOBsj9FEZ6LL3pRMldSvX3seqxfPY+/u\nnfz0S4udTQhhZS7crY7pzxft0Nl35uwul8++M6vl/nyd29VyTTTi+D4oiZ7CkAUNk5l+WqWzCQH8\nmj4Lfg1z1NdVceNFc7LabrxojtNftrZ4rbTF8X1QUknBB76VufBpmKMj0csPn3s7q+2Hz71t0zyN\ns2w/BePdzmswVKNnRVCjx91d7Wyap/FNHN8HJXNNwSc+7bzmk+Pd+delhLUb44KJ/j6wnoKjfBpL\n9mVToCk1+Yv0hbUb44qi2U9BRK4Qkf8QkTYRWZfn9yIi3wx+v0dEPh5lPOd/9TH2HjjG+V99LMqn\nGRfn3pGK9dw73I7Vp02BfLooPuTsdan3wdnr3H4fmGjteqODw8d72fVGR+TPFVlSEJFy4NvAlcA5\nwI0ick7OYVcCZwW3NcB3oopn3rrHOB58Tx3vTd131bx1j5EIRjQSfW7H2t7ZnXfxmouzperrqvIW\nG3S1NzZv3WMMDWz14fb7wETn09/dyfX37uTdEz1cf+9ObvruzkifL8qewkVAm6q+rqp9wCbg2pxj\nrgU2aspOYJqIzBrvQMJ6Bi72GMJ6Bq72GK799jMFtccp7EvVxS/bsJ6B9RhKy643OtjRlt07eLqt\nI9Ieg6hGs8hIRK4HrlDVzwb3bwIuVtVbM47ZCqxX1R3B/SeAtaq6K+dvrSHVk6ChoWHRpk2bCopl\n74EPyk431MDhjJPY8xrdGjrwKVbwK16LdWIkEgnq6uriDmNUXI/18PFe3j2Rqg6Q+T44fXI1DVMK\n6+EuX758t6q2jHScF7OPVPU+4D6AlpYWXbZsWUGP/6OvfjB0dPt5A2zYm/rPnlIFe36vsL8VtVvv\n+GDoKDPWuknwsmOxAvx+xplrZrwAbzoWr0+xrskYOsqMdRLwS8dizbV9+3YK/YzGxfVYd73Rwdp7\nU8NFme+Dhz/XQsv8+kieM8rhowNA5vLRpqCt0GPGbM/Xri6oPU4vfz1/TGHtcXtzff64wtrj5FOs\nvwyJKazdFKeW+fVctiD7y/+yBfWRJQSINim8AJwlIvNFZBLwKeDRnGMeBVYHs5AWA8dU9VAUwby5\n/mqGeltTqtz8Ihjy5vqrGdq4rG6S27HCyfG5HK9vsQ7tXzcJt2M10fn7zy7m4c8t5vTJ1Tz8ucX8\n/WcXR/uEqhrZDbgK+CXwK+B/BW03AzcHPwupGUq/AvYCLSP9zUWLFulYbNu2bUyPn0g+xarqV7wW\na3R8ireUYgV26Si+tyO9pqCqjwOP57Tdk/GzArdEGYMxxpjRsxXNxhhj0iwpGGOMSbOkYIwxJs2S\ngjHGmDRLCsYYY9IiK3MRFRE5Arw1hj8xA3hvnMKJmk+xgl/xWqzR8SneUor1TFWdOdJB3iWFsRKR\nXTqK+h8u8ClW8CteizU6PsVrsZ7Mho+MMcakWVIwxhiTVopJ4b64AyiAT7GCX/FarNHxKV6LNUfJ\nXVMwxhgTrhR7CsYYY0KURFIQkTkisk1EXhGRfSLyxbhjGo6IVIvI8yLyUhDv1+KOaSQiUi4ivwh2\n03OaiLwpIntFpFVEdo38iPiIyDQReVhEXhORV0VkSdwx5SMiHw1ez6HbcRH547jjGo6IfCn4fL0s\nIg+KSHXcMYURkS8Gce6L+nUtieGjYN/nWar6oohMBnYDv6Oqr8QcWl4iIkCtqiZEpBLYAXxRU/tY\nO0lEbgNagCmqek3c8QxHRN4kVabd+fnpIvID4GlV/W6wL8lpqno07riGIyLlpDbLulhVx7KmKDIi\n0kjqc3WOqnaLyGbgcVX9fryRnUxEziW1x/1FQB/wr6S2H2iL4vlKoqegqodU9cXg5xPAq0BjvFGF\nC8qfJ4K7lcHN2ewtIk3A1cB3446lmIjIVOATwP0AqtrnekIIXA78ytWEkKECqBGRCuA04GDM8YT5\nGPCcqr6vqgPAU8B/j+rJSiIpZBKRecCFwHPxRjK8YDimFXgX+HdVdTnevwa+AiTjDmSUFPipiOwW\nkTVxBzOM+cAR4O+Cobnvikht3EGNwqeAB+MOYjiqegD4v8DbwCFSuz7+JN6oQr0MXCYi9SJyGqnN\ny+aM8JhTVlJJQUTqgEeAP1bV43HHMxxVHVTVZlL7Vl8UdCGdIyLXAO+q6u64YynApcFreyVwi4h8\nIu6AQlQAHwe+o6oXAl3AunhDGl4wxLUSeCjuWIYjItOBa0kl3tlArYh8Ot6o8lPVV4E7gZ+QGjpq\nBQajer6SSQrB2PwjwAOq+qO44xmtYLhgG3BF3LGEWAqsDMbpNwErROQf4g1peMFZIqr6LvBPpMZq\nXdQOtGf0Eh8mlSRcdiXwoqoejjuQEfwW8IaqHlHVfuBHwCUxxxRKVe9X1UWq+gmgk9Q2x5EoiaQQ\nXLi9H3hVVe+KO56RiMhMEZkW/FwDfBJ4Ld6o8lPVP1XVJlWdR2rY4ElVdfKMC0BEaoPJBgRDMf+V\nVPfcOar6DrBfRD4aNF0OODk5IsONOD50FHgbWCwipwXfD5eTutboJBE5Pfj3XFLXE34Y1XNFukez\nQ5YCNwF7g3F6gD8L9pB20SzgB8EsjjJgs6o6P9XTEw3AP6W+B6gAfqiq/xpvSMP6AvBAMCzzOvAH\nMccTKkiynwQ+F3csI1HV50TkYeBFYAD4BW6vbn5EROqBfuCWKCcclMSUVGOMMaNTEsNHxhhjRseS\ngjHGmDRLCsYYY9IsKRhjjEmzpGCMMSbNkoIxYyQpO0Tkyoy2G0TE5amuxuRlU1KNGQdBGZKHSNXV\nqiA17/0KVf1VrIEZUyBLCsaMExH5Bqn6RLXACVX9i5hDMqZglhSMGSfBit4XSdW8b1HV3phDMqZg\npVLmwpjIqWqXiPwjkLCEYHxlF5qNGV9J/NlXwpiTWFIwxhiTZknBGGNMml1oNsYYk2Y9BWOMMWmW\nFIwxxqRZUjDGGJNmScEYY0yaJQVjjDFplhSMMcakWVIwxhiTZknBGGNM2v8HSI/ynuAxcdIAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6959cb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dmMaGKNedd0pZz+UKjAmX/xZc60rD1rIwxvhmuOMJ+TOYtm36ef99lVbk7eqJ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\nEsKJ9F3N2VMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa69293eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9xukejKbGyj5HYcLLuNBsxpJpToynOKUzSryjvFB2q9Py5ct3GGMWlft+M72P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\nh5FEimdfOU4qr95REc48dQL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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6931ca58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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V7BsnN46f2SX9kShfS5eTzlCqL7btOcCqJ7dwMJobtL/+0zMLMu289o/TuSGV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\niJA/3lbzuVmyZMnzxpjuUvv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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa695be358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa69657f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bW1GIcOaMFqjJBJontbi+x9W0h9NzaJan3PfS7l2oRf/iFUuXLt3FzN2l9qtn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\nEAxEKQiCIAgGohQEQRAEg/8fjz1u5QnMoJcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa696e69e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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nt7fA3JH36Qf24c+j47hg/nR1XYZqyfcopXMwM7t8fvVCnDlrinqcGy4+PVBn\nrlAe1erzqCSBKQUiuh9AN4DpRDQA4J8BxAGAme8G8CiASwH0ATgO4KNBtSUs/Laht7UksO7cDmx+\n8lV127quDldKyKwmPyyUgjLSHXdYs1nL0eS45fYWmDvyUpkcvvjIAQDA+uVzcOvas0z34xzj0jue\nQCwaQTbH+ML79R2t35QzU3F7z2dNaRQbtlATBBl99CGH7xnAdUGdv1L4MfLoOzKC3v4hzG2bhK17\nBnTfbe0ZwA0Xn+6pPAWgVyCj4xndKD8Wga48t5sR7JmzJltuT/7J2RG/eferWL9srul+yoxmvBC1\n87n/fEE1yfhtWvIjNNHqnlslBUaJAo3brzWTiFBdTPiM5lrjCz9/XjczMOR/FXXYdkpI2zkoCmT/\na8P42OYepDIntYIhktLVCPa4hb/i9bdSiKbznbmiiJiLwzUBoLd/CJd3deoU1olMVg3l1KIkvZVT\n8sGMMMugbO0ZwLbrL8DL+5629DWVS636Z4TqQZRCFdF3ZESnEIBii49bk4NV5zClqQEN0ShSmZO2\n7USUwERIRL2EI5qboj61tRefXJTBjRu347bLFmPXhlXY/YdBXH//c0X7Lu2cCkBvgun/83HTfRWC\nKPmQTOlzTZKpTCBlUPKztCya4lFfFYI22EESsoRyEaVQRezsO2q6PUrApIaY6/UM7EwiZuU5sszY\ncs35+OPgcSztnKo6ge1YNGsK4lEqGtWPZxlZZrVUwq4Nq7B6ySw8/cdBbN59UuGtXz4H05obdNeh\nlHkwmrO0uCn54MVhffDNZJF648L2cjpSuyCBYyUftRitIlQCCrSIM1vwiiiFKmJ6S4Pp9n/5wJlY\nWHC0ulnPwM4k0jGtqag8R46Bq77/tJqf8LXLnUfYbS0JfOODS/DpB/YhGiGkszlEI6QLz9R2SLeu\nPQvrl81Fb/8QlnZOxf7Db5leR1tLAt9ctxSffmAvohRBKpNFJEL57HGPJR8A56iqx182V8SPv3wU\nXfPabGXgJJ+gE8LMFKERcWYLXhGlUEUsf/t0RAg6J3CEgL9cNEMtR1DuGgVm5TlyBpv/TT/d68rk\nYBrhZDhnc0NUnQ3Mb2/F/PZWx+swOtABOPoJTCt/uoiqumjBdNyxva/oeBctmF60zStOgQDlOoTN\nFGFjPIJcjnWKcCLMEsR5Hh6iFKqItpYEvn3FUtz8070gIjAzvv7BJepL4NYp2taSwLtOm4Yn+gbV\nbe86bZoOgccdAAAcNUlEQVS6j2Otoyxj/2vDuOj0U1212RjhpETXrDu3A6vv3Fk0G3BzHUYHuteS\nD2a5GWay6prXhgvnt+lkdeH8trJmCcZ2+eX/MGIV4fXoJy6sujU9ykGc5+EiSqHKsBtdul13d/cf\nBnWdHAA80TeIviMjmN/e6iraJ1+0o7S2P717J7ZdfJ6a4W3m1/ASs1/KWsZmuRlW5/j3a5ah5+Ag\nHn/5KC5aMN03hWCF08prbmlrSWBdV4fOV7Ouq8OVT6hWkGqm4SNKoQqxGl062amVEZVVNe/e/iHM\nb2/VdZ7pTBaX/+uTRfvOmtJYctub4lGMjmctZwNLOqeaZgIrK48pprKBY2N44dAwvvyLA65HiaVm\nmHfN82924ITdymteOrrBZApbe6zzWCYCUs00fEQp1Bhu1t21QgkBBU52nnv7h5CIks7MYrcYjhGr\nUbzTbEB7HS8cGsaXt53s+Ned24Gte/JJXko7ShkleskwN15HkDbsBpuV17xQDx2mVDMNH1EKNYAf\ni+WsXz7H1KxQzmI4drZeN9E3yt9XbNqtMw8YczW0eO303GSYP9R7CLcUoqiyOcYV7zJfjlShXIWh\nrLxWbmRSPXSY9VjWu9KIUqhyylksJxGL4LPvPUNXgM5IqS+dna1XwSyKyJhf4WblNy1+d3qDyRRu\n/ulenV9FsdGbzU78cnr6USerXjrMWl6XoxYRpVDFeHGyWXUQbjqsUl46O9OFsV12nambxYoAoDkR\nRTbHvnd6+18btnC0n0R7XX46Pf2ok2V27yZi+KZUMw0PUQohEnRdnnJGVF5fOi8Zu07KzVgJ9h3t\nzfj9kVH187qu2bjq/LkBdXLOUVbaHI9qtOFr752EbwrlEql0A+qFh3oPYcXG7bj6nqewYuN2PNxr\nup6QjlJsxm0tCSzpnGpZ/mJv/xAGkynvF2ByntsuW4zGeAStiZht1U+lM9WidKaDyVRRJVitQgCA\nh/ceDmzUu2jWZMQMb0GEgESMdNcFAMNj42rlVoVqsuFrle9IKqOWGvHjfjudV/tc+fmcCeEjM4UQ\nKDXW2k+bcRAjyDVLZ2PhzMlq6Qorv4VThrWTTyHI0bhSVsOYMKidcWlLi+Q4X2q8KR6rOht+JWYy\nReXBC5FjMlOpXUQphIDXl9Ws5HU5NuKgEoDcKhon5eaYYR3waJwBEOXX1M4WkjwUk4yZ7BKxCO66\n6hwsmjU5NIWgrLFRqvINAjPZKGbAMBPNJqIPpZKIUggBLy+rVUdbzsMexAjSrirpWDqLwWRKd2wr\n5aYoDKUAXpZzuOJdnfjJM/3q5yBH48p15NeXKF6zwUx2DdEIpjTFQ+uAjGtsKKvWGQk7GqnSszxA\nfChBID6FEHBrfw/KJlzKCNLJLmzmJ+Ac49Lv7MTBN0dN/SZW/o782JwKPl8qbNB89tg2L9j5O4DK\n5wKYrbGxefer6DsyYrr/mqWzsWvDKtx7zfnYtWFVoB2km8ixsGYqYfpQJjoyUwgJN2agoGzCXkeQ\nbkZfHdOacCKjd7rms6L16yk4mQ5OjtRPXrOxEwwiT0B7HWadvra6ayVzAXr7hyy32+WehNE+s+dK\nWXK0UjOVaogGq3VEKYSI9mU1K6sQZHSLW9+EF/8Ds7v4frsX1IsJAvA3TwCAaUjsu06bVlTdddeG\nVRWxW2tLk7jZHjZmz9UNF58eiqwqPYubqIhSqAB2ERtBRre4GUG6HX0NHBtDLBpBxsZ84OYF9WKC\nKGVk6OSENAuJVSrMahXPrg2rsKQCHfH89lasXz6naNW6aqqEanyuKjlTqaZosFpFlELIuInYCCq6\nxa6D1K7z62b01dwQtS2+B+TLODu138oE8ZNnBtRaRHaRSnaKx42pqRqcpU4YV62rJoVQaaQEhv+I\nUggZN50QEXyPbskXfTsZ4fO1y5eoHWTRzMWFXXh0PFtUXdXI/U/368o4Wykl44u9s+8ofvJMP8D6\nZUO9jAzLWaXOSDWYJJRV64RipASGvwSqFIjoEgC3A4gCuIeZv2r4vhvAQwAOFjb9jJlvDbJNlcZN\nJ3QinXd0+sVgMoWbtvYi78vN+yw+tbVXLV5n7Dy39gxg2/UX2K7eZVZd1Yh2BTenUbsxL8AqRNRt\nwpyXVeoq6SwVhGojMKVARFEAdwF4D4ABAM8Q0cPMfMCw6xPMvDqodlQbxk4olc0hm83p+lYv6xm4\nYf9rbyFj0EOZXH77lKa4aec5Op61taEb8wvGM1lkTPUDeXJeO3Xm5VSNHc9mMTw27iqHoh7MNWGs\nIeHXMSVBLTyCnCmcB6CPmV8BACLaAmAtAKNSqDvMlo3MauzzxvUMyn8hrEbzXFYEhza/IBqNIJvJ\n6c4Ui+RrC1l19Lv/cBQn0jldx2vXnnKqxo6lM8gxcN19z9nOVIDaT4hy87yEUZ7CLznW+v2oNYJM\nXpsNoF/zeaCwzci7iWgfEf2SiBYF2J6qQknkUtZMtkpscyqk56YY2aJZUxCP6pPA4lHCollTPBW2\nM55XyS84Pp5FKpNDLEpoiAIRIiRihG+uWwoAGB5LYzyr7+hHxzO4/v5e3PzAPvzFtx7HFx56XpWL\nVXucEs2MKIlcd111DqKRCNJZdkxycpMQVc0F39wUXjS7xs1Pvlp0zX1HRkq+TreJZU6ylAS18CGn\nWPOSD0x0OYBLmPmawucPAzifma/X7DMZQI6Zk0R0KYDbmXmBybGuBXAtALS3t5+7ZcuWQNrslmQy\niZaWFl+Pmc0xxrM5NEQjiEZI3fbS6yPIae5RhAhnzGhFNEIYHktj4NgYFHfstOY4jo2m1c8d05ow\npSkOAOq+CtrvrM5vx1g6i4NvjiKraVuUCHPaJiE3Pobm5hYkUxm1fTlmgAgRADmY5zic3t6KRKFk\naSny8NrWeac0oyke9bSvUeZGObohiOcHcC8fs2s0EiECIz9qLOU63cjcTJbRbEonGy/3rh4o59lZ\nuXLlHmbuctovSPPRIQCdms8dhW0qzPyW5u9Hiei7RDSdmY8a9tsEYBMAdHV1cXd3d2CNdsOOHTsQ\nRhv29g/h7seewkgqo25rTcRwV9ciAIRbNvcgldG+GDnkffp5GuMZ7NpwkWn0D4CSTVKDyRT2vzaM\n2x/rKTiElfNFsGvDhXi+ZzfO6lqOFRu340T6ZHsSMcK/re/CK2+O4ouPFFsRv/6OBfirrs6i7VpG\new/p6iR97fIluNjBlDCYTOHGjdt1IbSN8Qh2rbnANDTXal8ARddklLEbgnp+rJ6Xey88W+cfMrtG\nJ7xep5PMB5MpU1netbJZJxsv964eCKPvCdJ89AyABUQ0j4gaAFwJ4GHtDkQ0g4io8Pd5hfYMBtim\nmqDvyAge6OlHOpMtKiVxPJ3Fxzb34OP/vkdXGsIMo2lFMVkppaC1Jga3JhHFPHHdfc+piXZmZicz\nU09DNIopTQ24QLNkp5alho7LrD1FdZJc4MVE5qf5yk/c3B+3/iGza1y/fI76uSEWQcJobvR4nU4y\nt5Kl0cxYqnlTKJ3AZgrMnCGi6wH8N/LD1x8w834i+njh+7sBXA7gH4goA2AMwJUclD2rRjBWxDR2\ne9kcI6sJLbXDrEMwc9be9NO9iFC+07Zz5FmVkb7pL08vWgfaroNqa0nYZulaORbN6iS5LXPhJcnJ\nat9KlVXwq0S5FrvyFErwgzYkrpTrtJO5lSwbosXjVElQC5dA8xSY+VEAjxq23a35+04AdwbZhlrC\nrCKmGw05qSGKHLOr+HqzSCBljeJUJm92sAsXNZLK5HDbf/0eX8VLus7KrKaQNsP51rVnYc3iWXj8\n5aO4aMF0dM1rA2CfdGY1UnWbbewlycls30qUVfC6FoaXDtSuPIVf12klcytZRode9nQcwX8ko7mK\nsKqIaUciRrj76nPUSCKnYmRukuesyjpYlbY4nj6ZZKasp9B3ZAT/8bRewf3HU6+qGc7a0e+mJ15R\nFYpdnoLZ+f1O9HMi7FFrKfWe/OhAw7hOs3Ps2GGuFITwkPUUqoi5bZNMtzdET9pTL5zfpvvuind1\n4qLTT1VfWsVvYNdhaG20iVikaI1iK1OBUtrCjvfe/jheeXMUl3z7ccuEObswQzsTzWvD5jMFq+1B\n4SRjP6lkJdAwrjNMWQruEKVQRcRjURj73CgB93ykC/decz62XX8BnvnTMd33W3sGPMdsaxdi+d1n\nVuGvz5uj+96qkJ1a2sKCE+kc0rl8+Kl5djMAsK3D1t6xaHVudw7nWkQcrULYiPmoQphlnXZMa0I8\nFtFlN8djEbVa6t7+IXBO39tyjkuq4KmtNWQsHb21Z0BXyE77G60deHQ8nyXsFiVhDrCvdmplulg0\nazJiEehmIErW9ERGHK1CmMhMoQJYZZ06jQqbG6JFVUlTWS7Lpm7nvDXjZJbw2UVZ0mbEo4RJDVEk\nYhF88f2L1OPedtliJGIR9Tvj6NfMrNDWksA31y1FIkaYFI+qWdP10EmKmUUIC5kphIxTNInZqLDv\nyAh6+4fQGI+iMR4pSuQpp3heKc7btpYEpjQ1oCEaVSOWzIhHCb/8xIUYHc/ihUPD+PIvDugqkQJc\nVB7bCRk1C0KwiFLwGadiZG6iSbTRI8a8BbNyDuU4Hc3WRXBTpdXMARqLABGKFGofRfC1yxdjfnsr\nBpMpXLFpt35hITVHobg8thGjTCU8URCCQ5SCj7hd8N5tNIlZ3kI2x0jEImiI+hMnb7YugrFKqxlm\nceb5FdOUGognj1fO6mZSIVMQwkWUgk+4TTLykgBllbfw2feegbPnTHM0n7gpoVxKQpZy3BXzp6sL\n2itZsKkMI8eMVIbV6y91dTOviVt+IvX7hXpFlIJPeEkycmsXX2qxyI2xpIQZXkbYXuz0Vsfd2z9k\nef1LOqeWtLqZW5n60YFrj7Gz72hdzE5E8QlmiFLwiSCSjOa3t9rWCLKilBG2Gzu93XGdrt+u1o6y\nz97+Ic+1hvwwL2mPMZ7NIsf50h9hz07CRMxyghWiFHzCixnGywt569qzPC8NWUppBDfYHVc7G4gS\nmSZZWdXasZKHk0y9Kj+zkbHZMYz4IbtqopJmOaH6EaXgI27MMKW8kPPbW12vEzyYTJmudOY0a3Fj\nSnA7G3h6907X9e5LCdFV8KL8rBSPGye4UXaVMLv4ec6gBg3CxECUgs84mWGCfCG1HV82l0M8SmiM\nRR2dx+WUZv786oVqQppy7U3xqOtr8Rqiq8Wtyc6r2SsWAaIR8wivSphd/D5nJespCdWPKIWQCeqF\nNF/rALjrqrPVCqpuf+dUmnnhzMno7R/Cn0fH8eVtB8rqrMqRh1uTnVuzl/YYZrOToM0ubs1b5Z6z\nlIgzoX4QpRAyQb2QZh2fstKZnzMXZdQapZMJbsbOygvlysONyc6N2UtRdFq/TanRUKXgxbzlxzkl\nM1ywQpRCBQjihSx1xO3ld9pRqxlOSzZa2cWd5OFkT3cy2TkpHrfmmTBneW6juspBMsMFM0QpVAi/\nX8hSR9xefufklFU6q2Mm3zl1vFby8MuebqV4vJhnwpzlOZm3pDMXgkKUwgSi1BmI2e+sSnubZSY3\nJ6LI5tiysyrVLu63Pd1M8Xg1z1RiliemHiFMRClMMEqdgWh/Zxydf/59C3Hm7CnomNZUHH2k+c7q\nvKXaxcMInSzFPFOJWZ6YeoSwEKUg6DAbnX/u5y+gJRFFpjAbUOoduR21huHvKBW3JqGgcxNkNiBU\nC6IUBB1WfoNk6mSJ610bVmGJRV0mM8Lwd5SDU4ccVm6CzAaEakCUgqDDqaKp0XzjdgTtp78jCKw6\nZCkJIdQbohQEHdrRuTYXQUFrvvE6gvbD3xE2UhJCqDcCVQpEdAmA2wFEAdzDzF81fE+F7y8FcBzA\n3zDzs0G0xWlEq/0egG7fnoODePzlo7howXTMO6UFY+ksBpMptLWcXCpTSXoyftZy80+exa9efAPv\neeepuPK809Rjds1r053/qk2/w0tvHMcZp07Cf31qZVHbte0ZOHYc255/HavPmoEPnNOp+27PH/+M\nn+87jA8snom/X7kA3/rvF/HQvtexdvEMnNLaiIf2HcbaxTNx9bvn6b678a/eiVwuh23Pv46ZkxPY\n8kw/cgxEKL+28i/3vYYHnzuEff3DyEKfvHb42HHEj45i4HcHcfW75+na8/PnBvDL/Ufw3kXt+Jf/\nswRfeeQFbHvhdaw+cwZOa2u2bM+8U1p012iU8b2/O6j+dtnbp+u+szu/8b6ayXhJx5SimdPYeAY/\n3HUQ7188ExcvnKG7P72vHsP/HDiCv1zYjosXzsBvDryu+9x3ZATHjqfRd2QE05obLCO+jo2OW14H\nAN2zo/2ua16b7XNvdw4jWjkPHR/XncPuO6tjzG9vLZKH8b3Tvlt+oW2DUeZuf+e29hjgzf9kt6/Z\nvQtCPkaI2f36uJ4OTBQF8L8A3gNgAMAzAD7EzAc0+1wK4B+RVwrnA7idmc+3O25XVxf39PR4aovT\niFb7/Vg6A6KTNYPmvK0J/3tkVHe8WxZncceLcXSdNg07+wbV7ae3N+v2Xb98Dm5dexYAYO5nfmHZ\nvne0N+NPf86PSEdSxWseN8YjatvN2qMQJyAdzO30xE1nZfCN52OIADZl5kqjKUYYy5y8SLtrnjm5\nAYffGnd1XALQkoiZynjG5Aa8bnGcmZMbcGwsY3rvjG2b0hjF8ImsKp9ohDApHi1aX2J0PIOc5nd2\n51eOqXDh/Db8+zXLABQ/9+vO7cDWPflzHE9nkdWcRPusAsXLwBqv2Uqu2vMbj2Fsq1Z2ynt346IM\n7ngx7pvfxtiGCAHNDTHHma3xd0b5WOFl9my3r9W9+8Q70yXLh4j2MHOX034RT0f1xnkA+pj5FWYe\nB7AFwFrDPmsBbOY8TwKYSkQz/WyE1iY8ksrgRDqHWx7ch8FkyvT7TC5fS1/Z16wDzjLjRDqnUwgA\nivbdvPtV9B0Zwc0/sZ/8/P7IqHp+M7Rtt1IIQHUoBC1+KwQAOoUA2F+zW4UA5BcPtZKxVYesnMPq\n3hnbpu0QgfzSqso5N+9+VT1OzvA7u/Mbj/lE3yB6Dg6aPvebnzx5jqzhJMqzCpgvA2u8ZiuU85sd\nw9hWreyU9055t7TvaKmYtSHHMO0HnH6nlY8VTn2N233t7p2f8rEiyJnC5QAuYeZrCp8/DOB8Zr5e\ns882AF9l5p2Fz78BsIGZewzHuhbAtQDQ3t5+7pYtW1y3YyydxcE3R5HVXGeUCPNOaUZTPGr6vRPt\nTcAR62oOOjqmTcLh4bGil3Ai40U+9UjQ8jm1tRGTm2Ken+uOaZMwbVIcx46nMXDseFnnb4hFSjqG\nIhvtO1oqTtdhdQ6r3ynyscKpr3G7LwDLe1eOfFauXOlqplATjmZm3gRgE5A3H3V3d7v+7WAyhRs3\nbtfV62mMR9R6/2bfO6FM/93w6xuXYdeOl/HA3sOuj1/reJFPPRK0fB74+y7MO6XF83P96xuXqX6x\nG7/1eFnnnzqpoaRjKLLRvqOl4nQdVuew+p0iHyuc+hq3+wKwvHd+yseKIM1HhwB0aj53FLZ53acs\nlGiaxngErYlY0Ypgxu9jESAeJXXfd7Q3Fx1TWVnswvl6p5pxX2XpzK9fcY5tG9/R3qye3wxt283a\noxAn29OEThAPV1NMf5F21zxzcoPr4xJgKWO7+zNzcoPld8a2TWnUj+qikZPP2frlc9TjRAy/s7sO\n4zEvnN+Grnltps+99hxRw0m0y7wqy8BaYdce5fxmxzC2VSs75b2zWrWvFMzaECGY9gNOv3OzDK5T\nX+N2X7t756d8rAjSfBRD3tF8MfId/TMA/pqZ92v2eR+A63HS0XwHM59nd9xSHM2Av9FHT+/eifOW\nXzCho4+0USIjJ9K6c2ijff40OKpGEH3u/Wfi3t8dxPihA2iYvXBCRB+Z3R9jhJHX6KPn9zyJs85d\nJtFHJtFH2nfLLyZS9FE58nHraA5MKRQacSmAbyMfkvoDZv4KEX0cAJj57kJI6p0ALkE+JPWjRn+C\nkVKVgp/s2LEDXkxY9YbIxx6RjzUiG3vKkY9bpRCo4ZeZHwXwqGHb3Zq/GcB1QbZBEARBcE+QPgVB\nEAShxhClIAiCIKiIUhAEQRBURCkIgiAIKqIUBEEQBJVAQ1KDgIjeBPCnCjdjOoCjFW5DNSPysUfk\nY43Ixp5y5HMaM5/itFPNKYVqgIh63MT71isiH3tEPtaIbOwJQz5iPhIEQRBURCkIgiAIKqIUSmNT\npRtQ5Yh87BH5WCOysSdw+YhPQRAEQVCRmYIgCIKgIkrBASLqJKLfEtEBItpPRDcUtr+NiH5FRC8X\n/p9W6bZWCiKKEtFzhZX0RDYaiGgqET1ARC8R0YtEtFzkk4eIbiy8Uy8Q0f1E1FjPsiGiHxDRG0T0\ngmabpTyI6LNE1EdEvyeiv/KrHaIUnMkAuImZFwJYBuA6IloI4DMAfsPMCwD8pvC5XrkBwIuazyKb\nk9wO4L+Y+QwAS5CXU93Lh4hmA/gEgC5mPhP58vpXor5l8yPklxHQYiqPQh90JYBFhd98l4hKX7tU\ngygFB5j5MDM/W/h7BPmXejaAtQB+XNjtxwA+UJkWVhYi6gDwPgD3aDaLbAAQ0RQAFwH4PgAw8zgz\nD0HkoxAD0FRYkGsSgNdQx7Jh5scB/Nmw2UoeawFsYeYUMx8E0AfAdoEyt4hS8AARzQVwNoCnALQz\ns7Lw8usA2ivUrErzbQC3ANAuKCuyyTMPwJsAflgwr91DRM0Q+YCZDwH4OoBXARwGMMzM/wORjREr\necwG0K/Zb6CwrWxEKbiEiFoAPAjgk8z8lva7wmJBdRfGRUSrAbzBzHus9qlX2RSIATgHwPeY+WwA\nozCYQ+pVPgXb+FrkFecsAM1EdLV2n3qVjRVhyUOUgguIKI68QriPmX9W2HyEiGYWvp8J4I1Kta+C\nrACwhoj+CGALgFVEdC9ENgoDAAaY+anC5weQVxIiH+AvABxk5jeZOQ3gZwDeDZGNESt5HALQqdmv\no7CtbEQpOFBYR/r7AF5k5m9qvnoYwEcKf38EwENht63SMPNnmbmDmeci7/TazsxXQ2QDAGDm1wH0\nE9E7CpsuBnAAIh8gbzZaRkSTCu/Yxcj760Q2eqzk8TCAK4koQUTzACwA8LQfJ5TkNQeI6AIATwB4\nHift5v+EvF9hK4A5yFdtXcfMRidR3UBE3QBuZubVRNQGkQ0AgIiWIu+EbwDwCoCPIj8Yq3v5ENGX\nAFyBfITfcwCuAdCCOpUNEd0PoBv5SqhHAPwzgJ/DQh5E9DkAf4u8/D7JzL/0pR2iFARBEAQFMR8J\ngiAIKqIUBEEQBBVRCoIgCIKKKAVBEARBRZSCIAiCoCJKQRA8QkRZIuotVPd8hIimFrbP1Va4LGz7\nIhHdXJmWCoJ3RCkIgnfGmHlpobrnnwFcV+kGCYJfiFIQhPLYDZ8KkQlCNRCrdAMEoVYp1K+/GIXS\n2AXeTkS9ms8zkK8GKgg1gSgFQfBOU6Hjn418vZ5fab77AzMvVT4Q0RdDbpsglIWYjwTBO2OFjv80\nAATxKQgTCFEKglAizHwc+SUlbyqsHiYINY8oBUEoA2Z+DsA+AB+qdFsEwQ+kSqogCIKgIjMFQRAE\nQUWUgiAIgqAiSkEQBEFQEaUgCIIgqIhSEARBEFREKQiCIAgqohQEQRAEFVEKgiAIgsr/B3pDVwiU\nQFQEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa697690b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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nXn2XpcfPm3Tj+0Yimhc4uugjoz5EEb7riimFOuD3gfA6UPkt5Qz+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\nnv8PbLeq+MaJjzMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6976f2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7gPOix99HtUw4OjiaqC4iEqq4TWGZu3/d3UejxzeAZSnmEhGROojbFAbM7ANm1hA9PkBK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\nd67VZ/xGnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa69887f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in df.describe().columns[:-2]:\n",
    "    df.plot.scatter(i,'Log-area',grid=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot boxplots of how the categorical features (month and day) affect the outcome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1aa699b0f28>"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PDwDd3d0tjs7MiqaWUUMC+oDBiPjHEcrsmcoh6eC03sfqGWiZLFmyhL6+Prq6upg8eTJd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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa69200438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.boxplot(column='Log-area',by='day')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1aa69b544a8>"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jTsx4syNir3KFGpYIxkLS6qjktulJGs8xp1bMIqyjY07ueD41ZGZWcE4EZmYF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa69b66780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.boxplot(column='Log-area',by='month')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data pre-processing, test/train split, REC function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from sklearn.preprocessing import LabelEncoder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Label encoder for the categorical feature (_day_ and _month_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LabelEncoder()"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enc = LabelEncoder()\n",
    "enc.fit(df['month'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['apr', 'aug', 'dec', 'feb', 'jan', 'jul', 'jun', 'mar', 'may',\n",
       "       'nov', 'oct', 'sep'], dtype=object)"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enc.classes_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>FFMC</th>\n",
       "      <th>DMC</th>\n",
       "      <th>DC</th>\n",
       "      <th>ISI</th>\n",
       "      <th>temp</th>\n",
       "      <th>RH</th>\n",
       "      <th>wind</th>\n",
       "      <th>rain</th>\n",
       "      <th>area</th>\n",
       "      <th>Log-area</th>\n",
       "      <th>month_encoded</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>mar</td>\n",
       "      <td>fri</td>\n",
       "      <td>86.2</td>\n",
       "      <td>26.2</td>\n",
       "      <td>94.3</td>\n",
       "      <td>5.1</td>\n",
       "      <td>8.2</td>\n",
       "      <td>51</td>\n",
       "      <td>6.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>oct</td>\n",
       "      <td>tue</td>\n",
       "      <td>90.6</td>\n",
       "      <td>35.4</td>\n",
       "      <td>669.1</td>\n",
       "      <td>6.7</td>\n",
       "      <td>18.0</td>\n",
       "      <td>33</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>oct</td>\n",
       "      <td>sat</td>\n",
       "      <td>90.6</td>\n",
       "      <td>43.7</td>\n",
       "      <td>686.9</td>\n",
       "      <td>6.7</td>\n",
       "      <td>14.6</td>\n",
       "      <td>33</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>mar</td>\n",
       "      <td>fri</td>\n",
       "      <td>91.7</td>\n",
       "      <td>33.3</td>\n",
       "      <td>77.5</td>\n",
       "      <td>9.0</td>\n",
       "      <td>8.3</td>\n",
       "      <td>97</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>mar</td>\n",
       "      <td>sun</td>\n",
       "      <td>89.3</td>\n",
       "      <td>51.3</td>\n",
       "      <td>102.2</td>\n",
       "      <td>9.6</td>\n",
       "      <td>11.4</td>\n",
       "      <td>99</td>\n",
       "      <td>1.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   X  Y month  day  FFMC   DMC     DC  ISI  temp  RH  wind  rain  area  \\\n",
       "0  7  5   mar  fri  86.2  26.2   94.3  5.1   8.2  51   6.7   0.0   0.0   \n",
       "1  7  4   oct  tue  90.6  35.4  669.1  6.7  18.0  33   0.9   0.0   0.0   \n",
       "2  7  4   oct  sat  90.6  43.7  686.9  6.7  14.6  33   1.3   0.0   0.0   \n",
       "3  8  6   mar  fri  91.7  33.3   77.5  9.0   8.3  97   4.0   0.2   0.0   \n",
       "4  8  6   mar  sun  89.3  51.3  102.2  9.6  11.4  99   1.8   0.0   0.0   \n",
       "\n",
       "   Log-area  month_encoded  \n",
       "0       0.0              7  \n",
       "1       0.0             10  \n",
       "2       0.0             10  \n",
       "3       0.0              7  \n",
       "4       0.0              7  "
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['month_encoded']=enc.transform(df['month'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LabelEncoder()"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enc.fit(df['day'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['fri', 'mon', 'sat', 'sun', 'thu', 'tue', 'wed'], dtype=object)"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enc.classes_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>FFMC</th>\n",
       "      <th>DMC</th>\n",
       "      <th>DC</th>\n",
       "      <th>ISI</th>\n",
       "      <th>temp</th>\n",
       "      <th>RH</th>\n",
       "      <th>wind</th>\n",
       "      <th>rain</th>\n",
       "      <th>area</th>\n",
       "      <th>Log-area</th>\n",
       "      <th>month_encoded</th>\n",
       "      <th>day_encoded</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>mar</td>\n",
       "      <td>fri</td>\n",
       "      <td>86.2</td>\n",
       "      <td>26.2</td>\n",
       "      <td>94.3</td>\n",
       "      <td>5.1</td>\n",
       "      <td>8.2</td>\n",
       "      <td>51</td>\n",
       "      <td>6.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>oct</td>\n",
       "      <td>tue</td>\n",
       "      <td>90.6</td>\n",
       "      <td>35.4</td>\n",
       "      <td>669.1</td>\n",
       "      <td>6.7</td>\n",
       "      <td>18.0</td>\n",
       "      <td>33</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>oct</td>\n",
       "      <td>sat</td>\n",
       "      <td>90.6</td>\n",
       "      <td>43.7</td>\n",
       "      <td>686.9</td>\n",
       "      <td>6.7</td>\n",
       "      <td>14.6</td>\n",
       "      <td>33</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>mar</td>\n",
       "      <td>fri</td>\n",
       "      <td>91.7</td>\n",
       "      <td>33.3</td>\n",
       "      <td>77.5</td>\n",
       "      <td>9.0</td>\n",
       "      <td>8.3</td>\n",
       "      <td>97</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>mar</td>\n",
       "      <td>sun</td>\n",
       "      <td>89.3</td>\n",
       "      <td>51.3</td>\n",
       "      <td>102.2</td>\n",
       "      <td>9.6</td>\n",
       "      <td>11.4</td>\n",
       "      <td>99</td>\n",
       "      <td>1.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>aug</td>\n",
       "      <td>sun</td>\n",
       "      <td>92.3</td>\n",
       "      <td>85.3</td>\n",
       "      <td>488.0</td>\n",
       "      <td>14.7</td>\n",
       "      <td>22.2</td>\n",
       "      <td>29</td>\n",
       "      <td>5.4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>aug</td>\n",
       "      <td>mon</td>\n",
       "      <td>92.3</td>\n",
       "      <td>88.9</td>\n",
       "      <td>495.6</td>\n",
       "      <td>8.5</td>\n",
       "      <td>24.1</td>\n",
       "      <td>27</td>\n",
       "      <td>3.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>aug</td>\n",
       "      <td>mon</td>\n",
       "      <td>91.5</td>\n",
       "      <td>145.4</td>\n",
       "      <td>608.2</td>\n",
       "      <td>10.7</td>\n",
       "      <td>8.0</td>\n",
       "      <td>86</td>\n",
       "      <td>2.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>sep</td>\n",
       "      <td>tue</td>\n",
       "      <td>91.0</td>\n",
       "      <td>129.5</td>\n",
       "      <td>692.6</td>\n",
       "      <td>7.0</td>\n",
       "      <td>13.1</td>\n",
       "      <td>63</td>\n",
       "      <td>5.4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>sep</td>\n",
       "      <td>sat</td>\n",
       "      <td>92.5</td>\n",
       "      <td>88.0</td>\n",
       "      <td>698.6</td>\n",
       "      <td>7.1</td>\n",
       "      <td>22.8</td>\n",
       "      <td>40</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>sep</td>\n",
       "      <td>sat</td>\n",
       "      <td>92.5</td>\n",
       "      <td>88.0</td>\n",
       "      <td>698.6</td>\n",
       "      <td>7.1</td>\n",
       "      <td>17.8</td>\n",
       "      <td>51</td>\n",
       "      <td>7.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>sep</td>\n",
       "      <td>sat</td>\n",
       "      <td>92.8</td>\n",
       "      <td>73.2</td>\n",
       "      <td>713.0</td>\n",
       "      <td>22.6</td>\n",
       "      <td>19.3</td>\n",
       "      <td>38</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>aug</td>\n",
       "      <td>fri</td>\n",
       "      <td>63.5</td>\n",
       "      <td>70.8</td>\n",
       "      <td>665.3</td>\n",
       "      <td>0.8</td>\n",
       "      <td>17.0</td>\n",
       "      <td>72</td>\n",
       "      <td>6.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>sep</td>\n",
       "      <td>mon</td>\n",
       "      <td>90.9</td>\n",
       "      <td>126.5</td>\n",
       "      <td>686.5</td>\n",
       "      <td>7.0</td>\n",
       "      <td>21.3</td>\n",
       "      <td>42</td>\n",
       "      <td>2.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>sep</td>\n",
       "      <td>wed</td>\n",
       "      <td>92.9</td>\n",
       "      <td>133.3</td>\n",
       "      <td>699.6</td>\n",
       "      <td>9.2</td>\n",
       "      <td>26.4</td>\n",
       "      <td>21</td>\n",
       "      <td>4.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    X  Y month  day  FFMC    DMC     DC   ISI  temp  RH  wind  rain  area  \\\n",
       "0   7  5   mar  fri  86.2   26.2   94.3   5.1   8.2  51   6.7   0.0   0.0   \n",
       "1   7  4   oct  tue  90.6   35.4  669.1   6.7  18.0  33   0.9   0.0   0.0   \n",
       "2   7  4   oct  sat  90.6   43.7  686.9   6.7  14.6  33   1.3   0.0   0.0   \n",
       "3   8  6   mar  fri  91.7   33.3   77.5   9.0   8.3  97   4.0   0.2   0.0   \n",
       "4   8  6   mar  sun  89.3   51.3  102.2   9.6  11.4  99   1.8   0.0   0.0   \n",
       "5   8  6   aug  sun  92.3   85.3  488.0  14.7  22.2  29   5.4   0.0   0.0   \n",
       "6   8  6   aug  mon  92.3   88.9  495.6   8.5  24.1  27   3.1   0.0   0.0   \n",
       "7   8  6   aug  mon  91.5  145.4  608.2  10.7   8.0  86   2.2   0.0   0.0   \n",
       "8   8  6   sep  tue  91.0  129.5  692.6   7.0  13.1  63   5.4   0.0   0.0   \n",
       "9   7  5   sep  sat  92.5   88.0  698.6   7.1  22.8  40   4.0   0.0   0.0   \n",
       "10  7  5   sep  sat  92.5   88.0  698.6   7.1  17.8  51   7.2   0.0   0.0   \n",
       "11  7  5   sep  sat  92.8   73.2  713.0  22.6  19.3  38   4.0   0.0   0.0   \n",
       "12  6  5   aug  fri  63.5   70.8  665.3   0.8  17.0  72   6.7   0.0   0.0   \n",
       "13  6  5   sep  mon  90.9  126.5  686.5   7.0  21.3  42   2.2   0.0   0.0   \n",
       "14  6  5   sep  wed  92.9  133.3  699.6   9.2  26.4  21   4.5   0.0   0.0   \n",
       "\n",
       "    Log-area  month_encoded  day_encoded  \n",
       "0        0.0              7            0  \n",
       "1        0.0             10            5  \n",
       "2        0.0             10            2  \n",
       "3        0.0              7            0  \n",
       "4        0.0              7            3  \n",
       "5        0.0              1            3  \n",
       "6        0.0              1            1  \n",
       "7        0.0              1            1  \n",
       "8        0.0             11            5  \n",
       "9        0.0             11            2  \n",
       "10       0.0             11            2  \n",
       "11       0.0             11            2  \n",
       "12       0.0              1            0  \n",
       "13       0.0             11            1  \n",
       "14       0.0             11            6  "
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['day_encoded']=enc.transform(df['day'])\n",
    "df.head(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test set fraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_size=0.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test/train split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_data=df.drop(['area','Log-area','month','day'],axis=1)\n",
    "y_data=df['Log-area']\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, test_size=test_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train=y_train.reshape(y_train.size,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression Error Characteristic (REC) estimation\n",
    "\n",
    "Receiver Operating Characteristic (ROC) curves provide a powerful tool for visualizing and comparing classification results. Regression Error Characteristic (REC) curves generalize ROC curves to regression. REC curves plot the error tolerance on the $x-axis$ versus the percentage of points predicted within the tolerance on the $y-axis$. The resulting\n",
    "curve estimates the cumulative distribution function of the error. The REC curve visually presents commonly-useds tatistics. The area-over-the-curve (AOC) is a biased estimate of the expected error. The $R^2$ value can be estimated using the ratio of the AOC for a given model to the AOC for the nul-model. Users can quickly assess the relative\n",
    "merits of many regression functions by examining the relative position of their REC curves. The shape of the curve reveals additional information that can be used to guide modeling.\n",
    "\n",
    "[Check this paper for more details](https://www.aaai.org/Papers/ICML/2003/ICML03-009.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rec(m,n,tol):\n",
    "    if type(m)!='numpy.ndarray':\n",
    "        m=np.array(m)\n",
    "    if type(n)!='numpy.ndarray':\n",
    "        n=np.array(n)\n",
    "    l=m.size\n",
    "    percent = 0\n",
    "    for i in range(l):\n",
    "        if np.abs(10**m[i]-10**n[i])<=tol:\n",
    "            percent+=1\n",
    "    return 100*(percent/l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the max tolerance limit for REC curve x-axis\n",
    "# For this problem this represents the absolute value of error in the prediction of the outcome i.e. area burned\n",
    "tol_max=20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gridsearch\n",
    "\n",
    "Finding the right parameters  for machine learning models is a tricky task! But luckily, Scikit-learn has the functionality of trying a bunch of combinations and see what works best, built in with GridSearchCV! The CV stands for cross-validation.\n",
    "\n",
    "**GridSearchCV takes a dictionary that describes the parameters that should be tried and a model to train. The grid of parameters is defined as a dictionary, where the keys are the parameters and the values are the settings to be tested.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Support Vector Regressor (SVR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.svm import SVR\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Parameter grid for the Grid Search\n",
    "param_grid = {'C': [0.01,0.1,1, 10], 'epsilon': [10,1,0.1,0.01,0.001,0.0001], 'kernel': ['rbf']}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid_SVR = GridSearchCV(SVR(),param_grid,refit=True,verbose=0,cv=5)\n",
    "grid_SVR.fit(scaler.fit_transform(X_train),scaler.fit_transform(y_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best parameters obtained by Grid Search: {'C': 0.01, 'epsilon': 1, 'kernel': 'rbf'}\n"
     ]
    }
   ],
   "source": [
    "print(\"Best parameters obtained by Grid Search:\",grid_SVR.best_params_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE for Support Vector Regression: 0.671031657615\n"
     ]
    }
   ],
   "source": [
    "a=grid_SVR.predict(X_test)\n",
    "print(\"RMSE for Support Vector Regression:\",np.sqrt(np.mean((y_test-a)**2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1aa6ae042e8>"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa680b9f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"Actual area burned\")\n",
    "plt.ylabel(\"Error\")\n",
    "plt.grid(True)\n",
    "plt.scatter(10**(y_test),10**(a)-10**(y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   1.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    2.,    0.,    1.,    0.,    0.,\n",
       "           1.,    1.,    6.,   12.,  183.]),\n",
       " array([ -1.09027396e+03,  -1.06845716e+03,  -1.04664036e+03,\n",
       "         -1.02482356e+03,  -1.00300676e+03,  -9.81189956e+02,\n",
       "         -9.59373156e+02,  -9.37556356e+02,  -9.15739556e+02,\n",
       "         -8.93922756e+02,  -8.72105956e+02,  -8.50289156e+02,\n",
       "         -8.28472356e+02,  -8.06655556e+02,  -7.84838756e+02,\n",
       "         -7.63021956e+02,  -7.41205156e+02,  -7.19388356e+02,\n",
       "         -6.97571556e+02,  -6.75754756e+02,  -6.53937956e+02,\n",
       "         -6.32121156e+02,  -6.10304356e+02,  -5.88487556e+02,\n",
       "         -5.66670756e+02,  -5.44853956e+02,  -5.23037156e+02,\n",
       "         -5.01220356e+02,  -4.79403556e+02,  -4.57586756e+02,\n",
       "         -4.35769956e+02,  -4.13953156e+02,  -3.92136356e+02,\n",
       "         -3.70319556e+02,  -3.48502756e+02,  -3.26685956e+02,\n",
       "         -3.04869156e+02,  -2.83052356e+02,  -2.61235556e+02,\n",
       "         -2.39418756e+02,  -2.17601956e+02,  -1.95785156e+02,\n",
       "         -1.73968356e+02,  -1.52151556e+02,  -1.30334756e+02,\n",
       "         -1.08517956e+02,  -8.67011561e+01,  -6.48843561e+01,\n",
       "         -4.30675561e+01,  -2.12507561e+01,   5.66043895e-01]),\n",
       " <a list of 50 Patch objects>)"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MK6tu9hmlfH5N2VnAWZ0Py8zMusXfjDUzK5wTvZlZ4ZzozcwK50RvZlY4J3ozs8I50ZuZ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\nCudEb2ZWuP8BFl02V35woVwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa69d6aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Histogram of prediction errors\\n\",fontsize=18)\n",
    "plt.xlabel(\"Prediction error ($ha$)\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.hist(10**(a.reshape(a.size,))-10**(y_test),bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aa6b01d5f8>]"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vIl3qrOY8CsDMvg6sBG4kXF/jXGD3kkQ3ANz37Cq+cMuTzHzbbtzw6SPYbbgu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\nRURSSMlZRCSF/n/Ofv2sKIbTRAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6af2d6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rec_SVR=[]\n",
    "for i in range(tol_max):\n",
    "    rec_SVR.append(rec(a,y_test,i))\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.title(\"REC curve for the Support Vector Regressor\\n\",fontsize=15)\n",
    "plt.xlabel(\"Absolute error (tolerance) in prediction ($ha$)\")\n",
    "plt.ylabel(\"Percentage of correct prediction\")\n",
    "plt.xticks([i*5 for i in range(tol_max+1)])\n",
    "plt.ylim(-10,100)\n",
    "plt.yticks([i*20 for i in range(6)])\n",
    "plt.grid(True)\n",
    "plt.plot(range(tol_max),rec_SVR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Tree Regressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(criterion='mae', max_depth=10, max_features=None,\n",
       "           max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
       "           min_impurity_split=None, min_samples_leaf=1,\n",
       "           min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "           presort=False, random_state=None, splitter='best')"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_model = DecisionTreeRegressor(max_depth=10,criterion='mae')\n",
    "tree_model.fit(scaler.fit_transform(X_train),scaler.fit_transform(y_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE for Decision Tree: 0.624177314982\n"
     ]
    }
   ],
   "source": [
    "a=tree_model.predict(X_test)\n",
    "print(\"RMSE for Decision Tree:\",np.sqrt(np.mean((y_test-a)**2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1aa6b0f3278>"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6aebab00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"Actual area burned\")\n",
    "plt.ylabel(\"Error\")\n",
    "plt.grid(True)\n",
    "plt.scatter(10**(y_test),10**(a)-10**(y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   1.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    2.,    0.,    1.,    0.,    0.,\n",
       "           1.,    1.,    6.,   12.,  183.]),\n",
       " array([-1089.64206016, -1067.82526016, -1046.00846016, -1024.19166016,\n",
       "        -1002.37486016,  -980.55806016,  -958.74126016,  -936.92446016,\n",
       "         -915.10766016,  -893.29086016,  -871.47406016,  -849.65726016,\n",
       "         -827.84046016,  -806.02366016,  -784.20686016,  -762.39006016,\n",
       "         -740.57326016,  -718.75646016,  -696.93966016,  -675.12286016,\n",
       "         -653.30606016,  -631.48926016,  -609.67246016,  -587.85566016,\n",
       "         -566.03886016,  -544.22206016,  -522.40526016,  -500.58846016,\n",
       "         -478.77166016,  -456.95486016,  -435.13806016,  -413.32126016,\n",
       "         -391.50446016,  -369.68766016,  -347.87086016,  -326.05406016,\n",
       "         -304.23726016,  -282.42046016,  -260.60366016,  -238.78686016,\n",
       "         -216.97006016,  -195.15326016,  -173.33646016,  -151.51966016,\n",
       "         -129.70286016,  -107.88606016,   -86.06926016,   -64.25246016,\n",
       "          -42.43566016,   -20.61886016,     1.19793984]),\n",
       " <a list of 50 Patch objects>)"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Fk+gjop1kNtqpHFaw+m1ltby6z3JJU0nTIw+20XfbxopV0qnAh/PN7wD/nq+3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\nwncAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b122588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Histogram of prediction errors\\n\",fontsize=18)\n",
    "plt.xlabel(\"Prediction error ($ha$)\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.hist(10**(a.reshape(a.size,))-10**(y_test),bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aa6b32abe0>]"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QaYGSxgDvAn4dLbc1eibU2cCt0WS3AudkWlYu1DY0M2HUMIaUxOk1cc7tDuL8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\n5pLJNwZZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b215e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rec_DT=[]\n",
    "for i in range(tol_max):\n",
    "    rec_DT.append(rec(a,y_test,i))\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.title(\"REC curve for the single Decision Tree\\n\",fontsize=15)\n",
    "plt.xlabel(\"Absolute error (tolerance) in prediction ($ha$)\")\n",
    "plt.ylabel(\"Percentage of correct prediction\")\n",
    "plt.xticks([i for i in range(0,tol_max+1,5)])\n",
    "plt.ylim(-10,100)\n",
    "plt.yticks([i*20 for i in range(6)])\n",
    "plt.grid(True)\n",
    "plt.plot(range(tol_max),rec_DT)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Forest Regressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "param_grid = {'max_depth': [5,10,15,20,50], 'max_leaf_nodes': [2,5,10], 'min_samples_leaf': [2,5,10],\n",
    "             'min_samples_split':[2,5,10]}\n",
    "grid_RF = GridSearchCV(RandomForestRegressor(),param_grid,refit=True,verbose=0,cv=5)\n",
    "grid_RF.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best parameters obtained by Grid Search: {'max_depth': 20, 'max_leaf_nodes': 2, 'min_samples_leaf': 10, 'min_samples_split': 5}\n"
     ]
    }
   ],
   "source": [
    "print(\"Best parameters obtained by Grid Search:\",grid_RF.best_params_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE for Random Forest: 0.614885707514\n"
     ]
    }
   ],
   "source": [
    "a=grid_RF.predict(X_test)\n",
    "rmse_rf=np.sqrt(np.mean((y_test-a)**2))\n",
    "print(\"RMSE for Random Forest:\",rmse_rf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1aa6b3e10f0>"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KYGXDetcCLwUOA77T0H4a8E9j7WfevHk5UV/96lcnvG0nsL7O1c21ZVpfOwA2ZBO/y9vx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\ngI4xAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b381cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"Actual area burned\")\n",
    "plt.ylabel(\"Error\")\n",
    "plt.grid(True)\n",
    "plt.scatter(10**(y_test),10**(a)-10**(y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   1.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    2.,    0.,    1.,    0.,    0.,\n",
       "           1.,    1.,    8.,   10.,  183.]),\n",
       " array([-1089.10040591, -1067.25515055, -1045.4098952 , -1023.56463984,\n",
       "        -1001.71938448,  -979.87412912,  -958.02887376,  -936.1836184 ,\n",
       "         -914.33836304,  -892.49310768,  -870.64785232,  -848.80259696,\n",
       "         -826.9573416 ,  -805.11208624,  -783.26683088,  -761.42157552,\n",
       "         -739.57632016,  -717.7310648 ,  -695.88580944,  -674.04055408,\n",
       "         -652.19529873,  -630.35004337,  -608.50478801,  -586.65953265,\n",
       "         -564.81427729,  -542.96902193,  -521.12376657,  -499.27851121,\n",
       "         -477.43325585,  -455.58800049,  -433.74274513,  -411.89748977,\n",
       "         -390.05223441,  -368.20697905,  -346.36172369,  -324.51646833,\n",
       "         -302.67121297,  -280.82595762,  -258.98070226,  -237.1354469 ,\n",
       "         -215.29019154,  -193.44493618,  -171.59968082,  -149.75442546,\n",
       "         -127.9091701 ,  -106.06391474,   -84.21865938,   -62.37340402,\n",
       "          -40.52814866,   -18.6828933 ,     3.16236206]),\n",
       " <a list of 50 Patch objects>)"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bDgLOqan+FuCmvNzye8AREfFoOwdsZmYbZzirbg4epHxunbLzgfNbH5aZmbWLvxlrZlY4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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b40cd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Histogram of prediction errors\\n\",fontsize=18)\n",
    "plt.xlabel(\"Prediction error ($ha$)\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.hist(10**(a.reshape(a.size,))-10**(y_test),bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aa6b622400>]"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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69Z3IQKRjy37w9Mp6xo0cyqGT9JRpkYFGSTTH3J0Fq+o4+aAJDBqkRyOLDDRx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b537ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rec_RF=[]\n",
    "for i in range(tol_max):\n",
    "    rec_RF.append(rec(a,y_test,i))\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.title(\"REC curve for the Random Forest\\n\",fontsize=15)\n",
    "plt.xlabel(\"Absolute error (tolerance) in prediction ($ha$)\")\n",
    "plt.ylabel(\"Percentage of correct prediction\")\n",
    "plt.xticks([i for i in range(0,tol_max+1,5)])\n",
    "plt.ylim(-10,100)\n",
    "plt.yticks([i*20 for i in range(6)])\n",
    "plt.grid(True)\n",
    "plt.plot(range(tol_max),rec_RF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deep network (using Keras (_TensorFlow_ backend))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "import keras.optimizers as opti\n",
    "from keras.layers import Dense, Activation,Dropout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_13 (Dense)             (None, 100)               1300      \n",
      "_________________________________________________________________\n",
      "activation_10 (Activation)   (None, 100)               0         \n",
      "_________________________________________________________________\n",
      "dropout_7 (Dropout)          (None, 100)               0         \n",
      "_________________________________________________________________\n",
      "dense_14 (Dense)             (None, 100)               10100     \n",
      "_________________________________________________________________\n",
      "dropout_8 (Dropout)          (None, 100)               0         \n",
      "_________________________________________________________________\n",
      "activation_11 (Activation)   (None, 100)               0         \n",
      "_________________________________________________________________\n",
      "dense_15 (Dense)             (None, 50)                5050      \n",
      "_________________________________________________________________\n",
      "activation_12 (Activation)   (None, 50)                0         \n",
      "_________________________________________________________________\n",
      "dense_16 (Dense)             (None, 1)                 51        \n",
      "=================================================================\n",
      "Total params: 16,501\n",
      "Trainable params: 16,501\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(100, input_dim=12))\n",
    "model.add(Activation('selu'))\n",
    "model.add(Dropout(0.3))\n",
    "model.add(Dense(100))\n",
    "model.add(Dropout(0.3))\n",
    "model.add(Activation('selu'))\n",
    "model.add(Dense(50))\n",
    "model.add(Activation('elu'))\n",
    "model.add(Dense(1))\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Learning rate and optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning_rate=0.001\n",
    "optimizer = opti.RMSprop(lr=learning_rate)\n",
    "model.compile(optimizer=optimizer,loss='mse')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Input data and mode fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1aa6b63ccc0>"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=X_train\n",
    "target = y_train\n",
    "model.fit(data, target, epochs=100, batch_size=10,verbose=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prediction and RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE for Deep Network: 0.610289206294\n"
     ]
    }
   ],
   "source": [
    "a=model.predict(X_test)\n",
    "print(\"RMSE for Deep Network:\",np.sqrt(np.mean((y_test-a.reshape(a.size,))**2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1aa6ba28d68>"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b74e978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"Actual area burned\")\n",
    "plt.ylabel(\"Error\")\n",
    "plt.grid(True)\n",
    "plt.scatter(10**(y_test),10**(a.reshape(a.size,))-10**(y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   1.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    0.,    0.,    0.,    2.,    0.,    1.,    0.,    0.,\n",
       "           1.,    1.,    6.,   12.,  183.]),\n",
       " array([-1089.03599032, -1067.21491772, -1045.39384512, -1023.57277251,\n",
       "        -1001.75169991,  -979.9306273 ,  -958.1095547 ,  -936.2884821 ,\n",
       "         -914.46740949,  -892.64633689,  -870.82526428,  -849.00419168,\n",
       "         -827.18311908,  -805.36204647,  -783.54097387,  -761.71990126,\n",
       "         -739.89882866,  -718.07775606,  -696.25668345,  -674.43561085,\n",
       "         -652.61453824,  -630.79346564,  -608.97239304,  -587.15132043,\n",
       "         -565.33024783,  -543.50917522,  -521.68810262,  -499.86703002,\n",
       "         -478.04595741,  -456.22488481,  -434.4038122 ,  -412.5827396 ,\n",
       "         -390.761667  ,  -368.94059439,  -347.11952179,  -325.29844918,\n",
       "         -303.47737658,  -281.65630398,  -259.83523137,  -238.01415877,\n",
       "         -216.19308616,  -194.37201356,  -172.55094096,  -150.72986835,\n",
       "         -128.90879575,  -107.08772314,   -85.26665054,   -63.44557794,\n",
       "          -41.62450533,   -19.80343273,     2.01763988]),\n",
       " <a list of 50 Patch objects>)"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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N9bcAN+Tllt8DDouIR9s5YDMzWz+jWXVz4DDlc+uUnQuc2/qwzMysXfzNWDOzwjnRm5kV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\nc6I3MyucE72ZWeGc6M3MCvf/AYreH+yIYlZWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b7c8710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Histogram of prediction errors\\n\",fontsize=18)\n",
    "plt.xlabel(\"Prediction error ($ha$)\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.hist(10**(a.reshape(a.size,))-10**(y_test),bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aa6b8d0c50>]"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gTklUpKIk6eKkRyYnoKuVRCpTkjZRSUBP+RSpTEqiA0Q3HxGpTEk6238rybhK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\n7CjiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b953fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rec_NN=[]\n",
    "for i in range(tol_max):\n",
    "    rec_NN.append(rec(a,y_test,i))\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.title(\"REC curve for the Deep Network\\n\",fontsize=15)\n",
    "plt.xlabel(\"Absolute error (tolerance) in prediction ($ha$)\")\n",
    "plt.ylabel(\"Percentage of correct prediction\")\n",
    "plt.xticks([i for i in range(0,tol_max+1,5)])\n",
    "plt.ylim(-10,100)\n",
    "plt.yticks([i*20 for i in range(6)])\n",
    "plt.grid(True)\n",
    "plt.plot(range(tol_max),rec_NN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relative performance of various models (REC curves)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1aa6baca6d8>"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TJ09m8uTJlY4tWrSozrYArF27ttqx8kUr7vzpT3/iT3/6k+t11ffs+uuvr3GV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\nIiIiFUhJoIiIiEgFUhIoIiIiUoH+H/LORDJL2+W8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1aa6b81a240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8))\n",
    "plt.title(\"REC curve for various models\\n\",fontsize=20)\n",
    "plt.xlabel(\"Absolute error (tolerance) in prediction ($ha$)\",fontsize=15)\n",
    "plt.ylabel(\"Percentage of correct prediction\",fontsize=15)\n",
    "plt.xticks([i for i in range(0,tol_max+1,1)],fontsize=13)\n",
    "plt.ylim(-10,100)\n",
    "plt.xlim(-2,tol_max)\n",
    "plt.yticks([i*20 for i in range(6)],fontsize=18)\n",
    "plt.grid(True)\n",
    "plt.plot(range(tol_max),rec_SVR,'--',lw=3)\n",
    "plt.plot(range(tol_max),rec_DT,'*-',lw=3)\n",
    "plt.plot(range(tol_max),rec_RF,'o-',lw=3)\n",
    "plt.plot(range(tol_max),rec_NN,'k-',lw=3)\n",
    "plt.legend(['SVR','Decision Tree','Random Forest','Deep NN'],fontsize=13)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
